@Article{EAJAM-1-108,
author = {Hui Ji, Zuowei Shen and Yuhong Xu},
title = {Wavelet Based Restoration of Images with Missing or Damaged Pixels},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {1},
number = {2},
pages = {108--131},
abstract = {<p style="text-align: justify;">This paper addresses the problem of how to restore degraded images where
the pixels have been partly lost during transmission or damaged by impulsive noise. A
wide range of image restoration tasks is covered in the mathematical model considered
in this paper – e.g. image deblurring, image inpainting and super-resolution imaging.
Based on the assumption that natural images are likely to have a sparse representation
in a wavelet tight frame domain, we propose a regularization-based approach to
recover degraded images, by enforcing the analysis-based sparsity prior of images in a
tight frame domain. The resulting minimization problem can be solved efficiently by
the split Bregman method. Numerical experiments on various image restoration tasks
– simultaneously image deblurring and inpainting, super-resolution imaging and image
deblurring under impulsive noise – demonstrated the effectiveness of our proposed algorithm.
It proved robust to mis-detection errors of missing or damaged pixels, and
compared favorably to existing algorithms.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.020310.240610a},
url = {http://global-sci.org/intro/article_detail/eajam/10923.html}
}